Rapidly mutating pathogens may be able to persist in the population and reach an endemic equilibrium by escaping hosts&rsquo; acquired immunity. For such diseases, multiple biological, environmental and population-level mechanisms determine the dynamics of the outbreak, including pathogen's epidemiological traits (e.g. transmissibility, infectious period and duration of immunity), seasonality, interaction with other circulating strains and hosts&rsquo; mixing and spatial fragmentation. Here, we study a susceptible-infected-recovered-susceptible model on a metapopulation where individuals are distributed in sub-populations connected via a network of mobility flows. Through extensive numerical simulations, we explore the phase space of pathogen's persistence and map the dynamical regimes of the pathogen following emergence. Our results show that spatial fragmentation and mobility play a key role in the persistence of the disease whose maximum is reached at intermediate mobility values. We describe the occurrence of different phenomena including local extinction and emergence of epidemic waves, and assess the conditions for large-scale spreading. Findings are highlighted in reference to previous studies and to real scenarios. Our work uncovers the crucial role of hosts&rsquo; mobility on the ecological dynamics of rapidly mutating pathogens, opening the path for further studies on disease ecology in the presence of a complex and heterogeneous environment.

RSOS160914F7: (a) Temporal evolution of the fraction of infected individuals (curve) and imported cases (points) in the largest population of the metapopulation system (k=91, N=2.5×105) for p=6×10−4 and duration of immunity L=320. (b) Temporal evolution of the fraction of infected individuals (curve) and imported cases (points) in the same patch for p=10−2 and duration of immunity L=320. Both panels show the results of a single stochastic run.

Mentions:
If persistence is enhanced locally for all patches, the resulting more synchronized system is, however, more prone to extinction of the epidemic for large enough immunity periods. This is the same type of phenomenon observed for measles in [26–28], i.e. a decrease in spatial heterogeneity reduces the effectiveness of the rescue effect by enhancing the level of synchronization. To test this hypothesis, we compared the local and importation dynamics occurring in the most connected patch in the intermediate and high mobility regimes. We considered a single stochastic run to highlight the critical role of stochastic effects within this mechanism (figure 7). Immunity is maintained equal in both scenarios, for comparison. When p=6×10−4 (intermediate mobility, figure 7a), importation of cases from neighbouring patches, desynchronized with respect to the local dynamics, allows the epidemic to survive the first wave and then quickly reach an endemic equilibrium, i.e. the rescue effect referred to before. If mobility is higher (p=0.01, figure 7b), importations are synchronized with the local dynamics, i.e. a peak of importations is occurring during the peak of the local epidemic wave, and both profiles fade out at the same time. In this way, there is no importation from outside the patch that could help sustain or relaunch the outbreak in the patch, and the epidemic goes extinct.Figure 7.

RSOS160914F7: (a) Temporal evolution of the fraction of infected individuals (curve) and imported cases (points) in the largest population of the metapopulation system (k=91, N=2.5×105) for p=6×10−4 and duration of immunity L=320. (b) Temporal evolution of the fraction of infected individuals (curve) and imported cases (points) in the same patch for p=10−2 and duration of immunity L=320. Both panels show the results of a single stochastic run.

Mentions:
If persistence is enhanced locally for all patches, the resulting more synchronized system is, however, more prone to extinction of the epidemic for large enough immunity periods. This is the same type of phenomenon observed for measles in [26–28], i.e. a decrease in spatial heterogeneity reduces the effectiveness of the rescue effect by enhancing the level of synchronization. To test this hypothesis, we compared the local and importation dynamics occurring in the most connected patch in the intermediate and high mobility regimes. We considered a single stochastic run to highlight the critical role of stochastic effects within this mechanism (figure 7). Immunity is maintained equal in both scenarios, for comparison. When p=6×10−4 (intermediate mobility, figure 7a), importation of cases from neighbouring patches, desynchronized with respect to the local dynamics, allows the epidemic to survive the first wave and then quickly reach an endemic equilibrium, i.e. the rescue effect referred to before. If mobility is higher (p=0.01, figure 7b), importations are synchronized with the local dynamics, i.e. a peak of importations is occurring during the peak of the local epidemic wave, and both profiles fade out at the same time. In this way, there is no importation from outside the patch that could help sustain or relaunch the outbreak in the patch, and the epidemic goes extinct.Figure 7.

Rapidly mutating pathogens may be able to persist in the population and reach an endemic equilibrium by escaping hosts&rsquo; acquired immunity. For such diseases, multiple biological, environmental and population-level mechanisms determine the dynamics of the outbreak, including pathogen's epidemiological traits (e.g. transmissibility, infectious period and duration of immunity), seasonality, interaction with other circulating strains and hosts&rsquo; mixing and spatial fragmentation. Here, we study a susceptible-infected-recovered-susceptible model on a metapopulation where individuals are distributed in sub-populations connected via a network of mobility flows. Through extensive numerical simulations, we explore the phase space of pathogen's persistence and map the dynamical regimes of the pathogen following emergence. Our results show that spatial fragmentation and mobility play a key role in the persistence of the disease whose maximum is reached at intermediate mobility values. We describe the occurrence of different phenomena including local extinction and emergence of epidemic waves, and assess the conditions for large-scale spreading. Findings are highlighted in reference to previous studies and to real scenarios. Our work uncovers the crucial role of hosts&rsquo; mobility on the ecological dynamics of rapidly mutating pathogens, opening the path for further studies on disease ecology in the presence of a complex and heterogeneous environment.